Is it permissible when visiting the grave of a deceased family member to "speak" to them as if they are there. To tell them how much they miss them, they love them. In general to express feelings, emotions, stories, etc.

Not to speak to them in a way that one would expect and answer. Or to speak in a way as if to request that they do something for them.

I have in mind that perhaps non-Jews are accustomed to doing such things, that's why I'm asking if there is anything in halacha that would prohibit such a thing.

2 Answers
2

The Chochmas Adam (Issur v'Heter, 89:7) decries the practice of going to a gravesite and unburdening oneself to the deceased by telling them about one's problems. However, he writes, this is not strictly a violation of consulting with the dead (see Deut. 18:11) since the communication is understood to go only one-way.

Before Rosh Hashanah, and especially on the day before the holiday
begins, it is a long-standing custom to visit gravesites and to exhort
the tzadikim there to intercede for us on the day of judgement.
However, we do not direct our prayers toward the dead who rest there;
rather, we implore G-d to have mercy on us for their sake. (Kitzur
Shulchan Aruch 128:13)

So it seems from this that as long as you are not pettitioning the dead its ok.